Geodesic
Cooperative differential games with the utility function switched at a random time moment
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 14 (2022) no. 2, pp. 31-50

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This paper describes a differential game of $n$ persons in which the utility functions of the players have a hybrid form, namely, they are changed at a random moment in time. With the help of integration in parts, the form of the payoff functional is simplified. For the cooperative scenario the problem of time-consistency of the optimality principle chosen by the players is studied and a solution is proposed in the form of an adapted imputation distribution procedure. The differential investment game is considered as an example.
Keywords: cooperative games, differential games, time-consistency problem, random duration, hybris differential games, imputation distribution procedure. 
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     author = {Anastasiia P. Zaremba},
     title = {Cooperative differential games with the utility function switched at a random time moment},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {31--50},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2022_14_2_a1/}
}
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Anastasiia P. Zaremba. Cooperative differential games with the utility function switched at a random time moment. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 14 (2022) no. 2, pp. 31-50. http://geodesic.mathdoc.fr/item/MGTA_2022_14_2_a1/